Measurement of Silicon Solar Cells under Natural Sunlight
W.M. Keogh, A.W. Blakers
Centre for Sustainable Energy Systems, Engineering Department, FEIT,
Australian National University, Canberra, ACT, 0200
AUSTRALIA
E-mail: William.Keogh@anu.edu.au
Abstract
The light source is very important when measuring solar cells. It is the major source of measurement
error and a good quality solar simulator is very expensive. Detailed modelling of natural sunlight
spectra and of silicon cells shows that measurement outdoors under natural sunlight can give better
accuracy than almost any simulator measurement. Periodic outdoor calibrations under natural
sunlight can therefore eliminate the need for an expensive solar simulator and greatly reduce the need
for calibration at international standards labs.
Solar spectra generated with the model SMARTS2 show that the direct solar spectrum under clear sky,
low air mass conditions is an excellent match to the standard AM1.5G spectrum - dramatically better
than simulators costing US$20k or more. Simulations of a broad range of silicon cells (efficiencies
6-25%) under the modelled direct spectra show that measurement errors of less than 5% are
achievable. The required conditions occur commonly in summer for all but polar latitudes
1. Introduction
Ideally, solar cells would be tested under a light source known to exactly match the standard spectrum
(i.e., have exactly the right irradiance and spectrum). However, no such light source exists. In practice,
cells are tested under a light source having approximately the right spectrum and a reference detector
is used to measure the irradiance. The deviation of the source spectrum from the standard spectrum
will cause an error, known as the spectral mismatch. The spectral mismatch, M, is defined as the ratio
of the measured short circuit current, Isc, under the non-ideal source spectrum to the ‘true’ value under
the standard spectrum. The measured Isc is corrected for non-standard irradiance using the reference
detector. The spectral mismatch error, εM = 1 − M , expresses the error in the cell measurement due
to spectral mismatch.
In general, the more similar the cell and the detector are, the more the source spectrum can deviate
from the standard. Conversely, the closer the source spectrum is to the standard spectrum, the wider
the range of cells that can be measured accurately. This is a very useful principle. Given a group of
similar cells, only a few of them need to be measured under a light source with good spectral matching
to the standard, and then only occasionally. These calibrated cells (known as reference cells) can then
be used to measure the rest of the group under a light source with poor spectral matching, which may
be much cheaper and/or more convenient than the good spectrum.
The best light sources available, even at international standards labs, are not an adequate match to the
standard solar spectrum. Spectral mismatch errors of several percent often result. Fortunately, it is
possible to almost eliminate the spectral mismatch error by determining M and then dividing the
measured value of Isc by M. This spectral mismatch correction procedure is used by most international
standards labs. If done with painstaking care, it is the most accurate way of measuring solar cells.
However, it requires very expensive equipment and a great deal of care in all the calibrations.
In contrast to solar simulators, natural sunlight, under the right atmospheric conditions, provides an
excellent match to the standard spectrum. Outdoor measurements should be significantly more
accurate than simulator measurements. Using natural sunlight for accurate cell measurements is not a
Measurement of Silicon Solar Cells under Natural Sunlight
Keogh & Blakers
new method – primary reference cells for space and terrestrial applications are usually calibrated
outdoors. For example, ASTM E1039-99 describes a calibration procedure using global radiation.
However, this requires specialised instrumentation and gives no error estimates. Other authors have
previously studied the accuracy of outdoor measurements. However, they have used only one cell, and
a good cell at that, and so may have significantly underestimated the worst case spectral mismatch.
To measure a cell with reference to the AM1.5 global standard spectrum, the obvious approach is to
measure it outdoors under global radiation. However, consideration of all the error sources involved
shows that measurement under direct radiation is more accurate under most conditions.
This work determines how large the spectral mismatch will be under a commonly occurring range of
atmospheric conditions for any likely silicon solar cell. Knowing the variation in the spectrum is not
sufficient to predict spectral mismatch, which is a complicated function of the spectrum and the cell
characteristics. There is no direct way to work out the characteristics of the worst sort of cell. So, to
determine the worst-case mismatch for given conditions, natural sunlight spectra were simulated for a
range of atmospheric conditions. A group of cells, representative of any silicon solar cell likely to be
made, were then simulated under each of the spectra and the resulting spectral mismatch values
calculated.
This paper presents simulation results only. It does not present a practical recipe, both because the
simulations have not yet been verified by experiments, and because there isn’t space for all the
practical details.
2. Solar Spectrum Modelling with SMARTS2
The solar spectrum at the surface of the earth, under clear skies, can be easily modelled on a desktop
computer using the recent code SMARTS2 (Gueymard 1995).
In addition, all atmospheric conditions that have a significant influence on spectral mismatch can be
adequately measured using non-specialist equipment.
2.1. Atmospheric Modelling and SMARTS2
In SMARTS2, the direct beam spectrum under clear skies is modelled as a series of independent
optical processes that attenuate extraterrestrial solar-radiation. The direct beam irradiance on a suntracking surface depends on approximately a dozen variables, the important ones (for this work) being:
air mass, turbidity, precipitable water, NO2 , and ozone.
Air Mass and pressure correction
Air mass, AM, is a measure of the optical path length through the atmosphere and is determined by the
zenith angle Z. The zenith angle is determined by the time and latitude. As is shown in section 7, low
air mass (AM 1.0-1.5) is necessary for low spectral mismatch. Most solar cell test sites are in the
temperate latitudes (30°-50°). For those closer to the equator, the desired low air mass conditions will
be available most of the year. For those further from the equator, they will be available at for at least a
few months around summer. The zenith angle Z can either be directly measured with an inclinometer,
or calculated from the latitude, longitude, time and date. There are numerous algorithms, including
SMARTS2, available to calculate the zenith angle. Reduced atmospheric pressure, due mostly to high
altitude, reduces the effective air mass, giving the pressure corrected air mass, AMp . As a rule-ofthumb, AM p reduces by 10% per 1000m altitude gained, eg at 1000 m & AM = 1, AMp = 0.9.
Turbidity
Turbidity characterises the scattering and absorption of light by small particles in the atmosphere. The
particles are mostly dust, water, ice, or hygroscopic salt particles. Turbidity is a difficult process to
quantify as the particles can vary in size, in number, and in other subtle ways. However, it can be
adequately described by two parameters, β and α. β is a measure of the ‘amount’ of turbidity and α
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characterises the particle size distribution (in other words, the ‘type’ of particles). The value of α
varies relatively little. This allows a simplification of the model by specifying typical α values for
different environments – eg Rural, Urban or Maritime. Turbidity is then reduced to a single parameter,
β. Rural aerosols have the smallest particles (largest α) and Maritime aerosols have the largest
particles. Urban aerosols are intermediate, but closer to rural. The larger the value of α, the more
spectrally selective the scattering is. With regard to the effect on spectral mismatch, the worst kind of
turbidity is that with the largest value of α. Hence, a rural aerosol model was used for this work.
The annual mean value of β in the tropics is ≈ 0.12 and in temperate zones ≈ 0.06. A subjective
description is: Clean 0.0, Clear 0.1, Turbid 0.2, Very turbid 0.4. In Australia turbidity is generally
lower: annual mean ≈ 0.024, peaking in September/October at ≈ 0.04 and as low as 0.01 in winter.
Accurate measurement of turbidity requires specialised instruments, but for this work, only a rough
estimate of turbidity is required. It is possible to determine turbidity with moderate accuracy using
only a broadband irradiance measurement. The only instrument required is a pyrheliometer, one of
which should cost around US$1500. The method is described in Gueymard (1998).
Precipitable water
Precipitable water, w, is the total amount of condensed water in a vertical column of the atmosphere.
In temperate locations, w is usually in the range 1-3cm. In tropical locations, w may be as high as 5cm.
In deserts or near freezing conditions, w may be as low as 0.5cm. Precise measurement of precipitable
water requires radiosonde balloon soundings. Surprisingly though, it is possible to estimate
precipitable water with sufficient accuracy using only ground level relative humidity and temperature.
The method is described in Gueymard (1994), and is accurate to ±20% provided w > 0.5cm.
NO2 and ozone
NO2 occurs naturally in the stratosphere and artificially in the troposphere in urban environments.
Stratospheric NO2 has little effect on the spectrum, but in polluted environments tropospheric NO2 can
have a major effect. Measuring NO2 requires specialised instrumentation. Fortunately, NO2 has a small
effect on spectral mismatch. This means that worst-case low and high levels of 0.1 and 5 matm-cm can
be assumed. Only in exceptionally clear conditions will it be below 0.1 matm-cm and only in
obviously smoggy, polluted conditions will it be over 5 matm-cm.
Ozone absorbs very strongly in the UV and weakly in the visible. The average amount of ozone is
0.34 atm-cm, and it is usually in the range 0.24-0.44 atm-cm. Measuring ozone requires specialised
instrumentation. Fortunately, ozone has a very small effect on spectral mismatch and a typical value of
0.34 atm-cm can be assumed.
2.2. Commercial Solar Simulator Spectra
Typical spectra for several commercial solar simulators were obtained to compare the quality of the
simulators to natural sunlight. The spectra were determined by measuring data points off printed
graphs. These spectra were then fed into PC1D exactly as the SMARTS2 modelled spectra were.
The solar simulators considered were: ELH Lamp – a cheap projector lamp; Oriel 1kW Solar
Simulator with AM1.5G filter – a continuous xenon arc solar simulator costing at least US$20,000;
and Spectrolab X-25 – the main simulator used at NREL, USA, costing around US$200,000.
3. Cell Modelling with PC1D
The spectral mismatch when testing a cell is dependent on both the source spectrum and the
characteristics of the cell. There is no direct way to determine what sort of cell will show the largest
mismatch error for a given spectrum and reference detector. To resolve this problem a set of cells was
created that is representative of almost any crystalline silicon cell likely to be made. All of these cells
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were then simulated under each spectrum and the cell with worst mismatch identified. The mismatch
error for this cell was then taken to be the worst mismatch error for the given spectrum.
The design parameters for the set of test cells, shown in Table 1, determine all the important
generation and recombination processes within solar cells. Other parameters are of secondary
importance. The values chosen for each of the parameters bracket the likely values to be found in a
silicon solar cell. Thus, conclusions drawn for the cells modelled are likely to hold for almost any
silicon solar cell. This set represents cells with performance in the range: Voc 530-700 mV,
Jsc 15-43 mA/cm2 , efficiency 6-25 %.
Table 1. Design parameters for the cell set.
Bulk Lifetime (n & p)
Front Surface Recombination
Rear Surface Recombination
Thickness
Front and Rear internal reflectivity
Texturing
Front surface coating
Cell base resistivity
Diffusions
Material properties
Excitation
0.1, 30, 10 000 µs
103 , 107 cm/s
103 , 107 cm/s
30, 100, 500 µm
50, 100%
Textured, or polished
bare silicon, bare silicon behind glass, optimal SLAR
(Single Layer Anti-Reflection coating), optimal SLAR
behind glass, optimal DLAR, optimal DLAR behind glass
1 ohm-cm (n+/p/p+)
gaussian profile, 0.8 microns deep, maximum doping of
3x1019 cm-3 (100Ω/sq)
as for single crystal silicon
25°C
4. Calculation of Spectral Mismatch
For each spectrum generated with SMARTS2, PC1D simulated the current of every cell in the cell set.
PC1D was also run to simulate the current of every cell under the reference spectrum. The spectral
mismatch, M, was then calculated for every cell under every spectrum. Two possible reference
detectors were considered: a pyrheliometer (a thermal detector used for measuring direct beam
irradiance), and a high quality cell in the cell set.
The accuracy of natural sunlight testing is limited by how accurately the spectral mismatch can be
determined. In this work, the spectral mismatch is predicted using the cell model, PC1D, and the
spectrum model, SMARTS2. The accuracy of PC1D is not a limitation as PC1D is only used to predict
the mismatch distribution for a representative set of cells. The accuracy of SMARTS2 was examined
by Gueymard (1995) and he found that it was accurate to within the limits of a LiCor LI-1800
spectroradiometer (approximately ±5% between 420 nm and 1100 nm). Field (Field and Emery 1993)
found that use of a LiCor LI-1800 to measure the spectrum of natural sunlight could result in 0.2%
error in spectral mismatch prediction. Consequently, prediction of spectral mismatch from SMARTS2
should be accurate to approximately ±0.2%. However, the error estimates used by Field were for an
unlikely worst case, whereas the predictions of SMARTS2 were only just within LiCor LI-1800 error
limits. Consequently the ±0.2% error estimate is probably optimistic. For this work, a more
conservative
value
of
±0.4%
is
used.
So
M ≈ 1±0.004,
hence
εM ≈ 1 − (1 ± 0.004) ≈ 0 ± 0.004 = (0 ± 0.4)% , eg, M = 0.95±(0.4%) leads to ε M = (5±0.4)%.
5. Determining Importance of Atmospheric Parameters
The spectral mismatch under natural sunlight is dependent on the sunlight spectrum, which in turn is
dependent on a range of atmospheric parameters. In SMARTS2, the direct beam spectrum is affected
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by 12 model parameters. Systematically varying all of these parameters over typical ranges would
require a huge number of tests. In addition, it would be very hard to make sense of the resulting 12dimensional variation. As a first step, a sensitivity analysis was conducted to work out the relative
importance of the different parameters and hence reduce the number of variables. The sensitivity
analysis showed that:
1) Ozone, season, latitude, and temperature have minimal influence on the mismatch and can be
ignored. It may seem surprising that ozone has so little effect on spectral mismatch, but in terms of
the total number of photons (which determines cell current), its impact is in fact relatively small.
2) NO2 has a small, but still significant effect on the mismatch.
3) Precipitable water, turbidity, air mass and altitude have a major influence on the mismatch.
6. Simulation results
Having determined which atmospheric parameters were important, a detailed simulation was run. The
865 cells in the cell set were simulated under 1350 spectra, requiring over 1 million PC1D runs.
Contour plots of the resulting spectral-mismatch errors, ε M, are shown below.
w = 0.5 atm-cm
w = 1.0 atm-cm
0.2
0.2 7
7
5
0.15
12
6
0.1
9
8
7
6
0.05
1
5
1
1.5
2
Press. Corr. AM, AMp
10
9
4
12
10
9
6
8
0.15
Turbidity, β
ε M ± 0.4
7
0.1
O 3 = 0.34 atm-cm
2
0.1
6
5
3
8
7
3
Turbidity, β
2
w = 5.0 atm-cm
0.2
4
0
1.5
Press. Corr. AM, AMp
w = 3.0 atm-cm
NO 2 = 0.1, 1, 5 matm-cm
5
2
1
1
Ref. Det. = pyrheliometer
all cells included
0.05
6
.
4
4
1
6
2
5
2
0.2
0
7
3
0.05
5
1.5
Press. Corr. AM, AMp
0.05
8
0.1
4
3
0
1
0.15
5
4
2
4
3
0
15
7
1.5
1
10
9
8
7
6
6
9
15
12
6
Turbidity, β
Turbidity, β
Turbidity, β
15
8
0.05
10
9
0.15
9
0.1
8
10
12
8
10
0.15
w = 2.0 atm-cm
0.2
20
6
5
0
1.5
2
5
Press. Corr. AM, AMp
1
1.5
7
2
Press. Corr. AM, AMp
Figure 1. Contour plots of worst-case ε M (%). Ref. det.: Pyrheliometer, Std. spectrum: AM1.5G.
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w = 0.5 atm-cm
w = 1.0 atm-cm
0.2
0.2
0.05
3
2
2
1
1.5
7
4
6
5
1
1.5
2
εM ± 0 . 4
8
0.15
Ref. Det: Excellent silicon cell
All cells included
5
0.1
4
For solar simulators:
E L H - εM = 1 6 %
2
3
NO2 = 0.1, 1, 5 matm-cm
5
1.
Turbidity, β
5
O3 = 0.34 atm-cm
6
3
2
6
5
4
0.05
Oriel - ε M = 1 6 %
X25 - εM = 3 %
3
0
0
1
1.5
Press. Corr. AM, AMp
7
4
Turbidity, β
2
9
10
7
1.
1
10
12
0.1
1
6
5
4
3
w = 5.0 atm-cm
3
0.05
7
2
Press. Corr. AM, AMp
0.2
8
8
3
0
w = 3.0 atm-cm
0.15
4
0.1
0.05
0
1.5
9
Turbidity, β
Turbidity, β
Turbidity, β
9
8
7
6
5
4
Press. Corr. AM, AMp
0.2
9
10
5
12
5
1
0.1
10
6
5
4
6
3
12
7
7
10
9
8
7
6
0.15
8
0.15
12
0.05
0
8
7
15
8
0.1 6
w = 2.0 atm-cm
0.2
15
9
10 9
0.15
Keogh & Blakers
1.5
2
Press. Corr. AM, AMp
1
1.5
2
Press. Corr. AM, AMp
Figure 2. Contour plots of worst-case ε M (%). Ref. det.: Silicon cell, Std. spectrum: AM1.5G.
7. Discussion
Good testing conditions can be identified from the mismatch error plots: the lower the air mass the
better, and the lower the turbidity the better, except in the presence of high precipitable water. The
effects of turbidity and precipitable water tend to cancel, so higher turbidity is tolerable in the presence
of higher precipitable water. Fortunately, nature provides this correlation – both turbidity and
precipitable water are higher in summer. For temperate latitudes in summer, air mass close to 1.0,
turbidity below 0.05, and precipitable water in the range 1-3 cm will occur commonly. For these
conditions, the worst-case spectral mismatch will be < 3%. Including pyrheliometer error of
approximately 1%, a total measurement error of little more than 3% should be achievable. This is
comparable to the best simulator measurement possible. Testing in midwinter is less attractive. Air
mass will be high, and precipitable water will be low, so achieving mismatch < 6% will be difficult.
The accuracy and convenience of natural sunlight testing eliminates the need for an expensive solar
simulator. Reference cells identical to the technology currently being produced can easily be made.
Using them, spectral mismatch under a cheap simulator (eg ELH lamps) will be minimal. All routine
measurements can be done indoors, with only occasional re-calibrations outdoors.
The worst-case spectral mismatch errors for three solar simulators, as well as for natural sunlight, are
shown in Figure 2. The ELH and Oriel simulators are very similar at 16%. Measurement outdoors
under just about any conditions will give a better result then using one of these simulators. The
Spectrolab X25 gives a mismatch error of 3%. Measurement outdoors should equal or better this under
good conditions, but could be significantly worse under bad conditions. It is surprising that the Oriel
simulator performs so poorly, but examination of its spectrum shows too much blue and too little IR.
Figure 2, where the reference detector is a silicon cell, shows a slightly lower spectral mismatch than
Figure 1, where the reference detector is a pyrheliometer. However, the difference under good
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conditions is only about 1 to 2% absolute. Pyrheliometers are significantly more accurate than
calibrated cells (1% vs. ~3%), so the total error is likely to be smaller if a pyrheliometer is used.
Measurement of cells under natural sunlight has significant advantages over simulator measurements:
§ Cheap, simple, and quick – the only expensive instrument required is a pyrheliometer
§ Easy access to accurate measurements without sending cells to distant measurement facilities
§ Superb light uniformity over any area
§ Much smaller spectral mismatch than any affordable simulator without mismatch correction
§ Vastly cheaper than spectral mismatch correction, and much less opportunity for mistakes
Experimental verification of this modelling is in progress. Definitive measurements will not be
available until mid-summer when AM1 is possible, but preliminary measurements are encouraging. Jsc
for six silicon cells was measured outdoors under global radiation (not direct-beam) for air masses
ranging from 1 to 2.7. The cells ranged in quality from high performance devices to multicrystalline
cells with effective diffusion lengths of about 30 µm. Clear skies prevailed during the measurements.
The variation in short circuit current of the 6 test cells relative to the reference cell (a good quality
silicon cell) was less than ±2%, which supports the conclusions of the PC1D modelling.
8. Conclusions
Simulations of spectral mismatch when testing silicon solar cells outdoors show that natural sunlight
can give more accurate measurements than all but the most painstaking simulator measurements. Use
of this method can eliminate the need for an expensive solar simulator.
9. References
Field, H. and Emery, K. (1993). An uncertainty analysis of the spectral correction factor. Proceedings
of 23rd IEEE Photovoltaic Specialists Conference, Louisville, KY, USA. pp1180-7.
Gueymard, C. (1994). Analysis of monthly average atmospheric precipitable water and turbidity in
Canada and northern United States. Solar Energy 53(1): 57-71.
Gueymard, C. (1995). SMARTS2, a Simple Model of the Atmospheric Radiative Transfer of Sunshine,
Florida Solar Energy Centre Report FSEC-PF-270-95.
Gueymard, C. A. (1998). Turbidity Determination from Broadband Irradiance Measurements - A
Detailed Multicoefficient Approach [Review]. Journal of Applied Meteorology 37(4): 414-435.
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